The Metropolitan Police launched an investigation into Savile’s activities, known as Operation Yewtree, after an ITV documentary in October exposed him as a serial sexual abuser.

Another 12 inquiries are under way, including two BBC reviews, one looking at whether the Corporation’s culture and practices allowed Savile to continue abusing children and the other examining why Newsnight dropped a report about his sexual attacks.

Detectives are also examining allegations against other figures from the entertainment world and have already questioned seven suspects, among them publicist Max Clifford, singer Gary Glitter, comedian Freddie Starr and DJ Dave Lee Travis.

So far 589 people have contacted the Operation Yewtree team with information relating to Savile and others.

Police warned that there would be further arrests around the country in the coming weeks.

A Scotland Yard spokesman said: “Our officers will continue to investigate allegations made against those who potentially can be brought to justice.”

The Metropolitan Police and the NSPCC children’s charity are now compiling a report outlining the full extent of Savile’s sexual abuse, which is due to be published early in the New Year.

Commander Spindler, head of Scotland Yard’s specialist crime investigations, said: “Once again I want to pay tribute to those who have spoken out and bravely shared their experiences of sexual assault.

“As a result of their collective efforts we have a great opportunity to learn from the past, develop our understanding of sexual exploitation and improve our safeguarding procedures.

“Our response should send a clear warning to anyone today now in a position of power and influence who abuse their status to sexually exploit children and young people - victims will be listened to and robust action taken.”

Publicity about the Savile scandal has led to a dramatic rise in people reporting sexual abuse to the police, with a four-fold increase recorded in London since the launch of Operation Yewtree.

The NSPCC has received 236 calls about Savile since the start of October, an average of five a day.

Peter Watt, director of the charity’s helpline, said: "Sadly, Savile's victims had to wait decades for help. We have a historic opportunity to learn from the past and make a difference to how we protect children today."